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Thinking about gravitational RedShift
There are at least two ways of calculating and three ways of thinking about
gravitational redshift. Consider a massive body, say a planet sized non-rotating spherical body. We have a space observer that can measure a beam of light emitted from the massive body. The beam of light emitted from the surface of the planet will have a lower measured frequency and a correspondingly longer wavelength as measured by the space observer. We can think of this as: 1) a clock on the surface of the massive object runs slower than a clock the space observer may have. Any measure of frequency is done against a clock (directly or indirectly) and so the frequency of the wave will be lower. We assume that neither the space observer or planet observer notice anything unusual about their respective clocks (local time does not seem to be running faster/slower) so the lower frequency of the light beam will appear red shifted if in the visible range. 2) As spacetime around the planet is curved, the light beam is correspondingly stretched as it passes over the expanded spacetime. Thus the wavelength of the light will be longer as measured by the space observer. 3) As gravity exerts a force on all objects moving away from the gravitating body, objects require a force to move (ie to accelerate away from the gravitating body). Photons lose energy as they move away from a gravitating body. A loss of energy of a photon corresponds to a lower frequency and longer wavelength of a light beam. When discussing light attempting to escape from a black hole, we hear explanations corresponding to (2) and (3) but not (1). Why? Let us consider a simple test of the three mentioned above. Clocks on the surface of the sphere and in space are partially synchronised in the following way: A signal is sent from the planet based clock at 12:00 exactly (to the highest available precision). The space based clock is zeroed to 12:00 exactly when the light beam reaches it. The planet clock sends a second signal after 100 hours exactly. The space based clock stops upon receipt of the signal. If the only cause of redshift is the loss of energy of photons or the stretching of wavelength, as in (2) and (3), then the space based clock will stop exactly 100 hours after it starts. If the planet based clock is actually running slower then more than 100 hours will be measured by the space based clock. It is my understanding that clocks near massive bodies do in fact run slower in a measurable way and that atomic clocks at higher altitude on Earth require periodic adjustment due to their faster pace as compared to sea level clocks. If this is correct then (2) and (3) are only valid for instantaneous measurements, ie snapshots of space-time. As there are three ways of looking at redshift, any theory of redshift and its causative agent should also account for (1) eg the non-emission of light from black holes (clocks on the surface of the Black Hole must be actually and physically frozen relative to a space observer) and the redshift of the objects at great distances (if the stretching of space time is offered in the form of (2) ie light stretched as it passes over expanding space-time). -- Kind Regards Robert Karl Stonjek |
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